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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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| subroutine sggbal | ( | character | JOB, |
| integer | N, | ||
| real, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| real, dimension( ldb, * ) | B, | ||
| integer | LDB, | ||
| integer | ILO, | ||
| integer | IHI, | ||
| real, dimension( * ) | LSCALE, | ||
| real, dimension( * ) | RSCALE, | ||
| real, dimension( * ) | WORK, | ||
| integer | INFO | ||
| ) |
SGGBAL
Download SGGBAL + dependencies [TGZ] [ZIP] [TXT]
SGGBAL balances a pair of general real matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x.
| [in] | JOB | JOB is CHARACTER*1
Specifies the operations to be performed on A and B:
= 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
and RSCALE(I) = 1.0 for i = 1,...,N.
= 'P': permute only;
= 'S': scale only;
= 'B': both permute and scale. |
| [in] | N | N is INTEGER
The order of the matrices A and B. N >= 0. |
| [in,out] | A | A is REAL array, dimension (LDA,N)
On entry, the input matrix A.
On exit, A is overwritten by the balanced matrix.
If JOB = 'N', A is not referenced. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N). |
| [in,out] | B | B is REAL array, dimension (LDB,N)
On entry, the input matrix B.
On exit, B is overwritten by the balanced matrix.
If JOB = 'N', B is not referenced. |
| [in] | LDB | LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N). |
| [out] | ILO | ILO is INTEGER |
| [out] | IHI | IHI is INTEGER
ILO and IHI are set to integers such that on exit
A(i,j) = 0 and B(i,j) = 0 if i > j and
j = 1,...,ILO-1 or i = IHI+1,...,N.
If JOB = 'N' or 'S', ILO = 1 and IHI = N. |
| [out] | LSCALE | LSCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied
to the left side of A and B. If P(j) is the index of the
row interchanged with row j, and D(j)
is the scaling factor applied to row j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1. |
| [out] | RSCALE | RSCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied
to the right side of A and B. If P(j) is the index of the
column interchanged with column j, and D(j)
is the scaling factor applied to column j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1. |
| [out] | WORK | WORK is REAL array, dimension (lwork)
lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
at least 1 when JOB = 'N' or 'P'. |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value. |
See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. Definition at line 179 of file sggbal.f.
1.8.10